Problem: Solve for $x$ and $y$ using substitution. ${-5x-2y = 5}$ ${x = y+6}$
Since $x$ has already been solved for, substitute $y+6$ for $x$ in the first equation. ${-5}{(y+6)}{- 2y = 5}$ Simplify and solve for $y$ $-5y-30 - 2y = 5$ $-7y-30 = 5$ $-7y-30{+30} = 5{+30}$ $-7y = 35$ $\dfrac{-7y}{{-7}} = \dfrac{35}{{-7}}$ ${y = -5}$ Now that you know ${y = -5}$ , plug it back into $\thinspace {x = y+6}\thinspace$ to find $x$ ${x = }{(-5)}{ + 6}$ ${x = 1}$ You can also plug ${y = -5}$ into $\thinspace {-5x-2y = 5}\thinspace$ and get the same answer for $x$ : ${-5x - 2}{(-5)}{= 5}$ ${x = 1}$